Etymologiae, Book III, chapter 5: De prima divisione parium et imparium
Chapter V. On the first division of even and odd Number is divided into these, even and odd. Even number is divided into these: evenly even, evenly odd, and unevenly even. Odd number is divided into these: first and simple, second and composite, third middle; which in one way is first and uncompounded, in another way second and compounded. An even number is one that can be divided into two equal parts, as II, VIII. An odd number is one that cannot be divided into equal parts, one in the middle either lacking or exceeding, as III, V, VII, IX and the rest. An evenly even number is one that is divided evenly by even numbers until it comes to the indivisible unit; as for example 64 has half 32, this 16, 16 is 8, 8 is 4, 4 is 2, 2 is 1, which is single and indivisible. An evenly odd number is one that receives division into equal parts, but whose parts soon remain indivisible, as VI, X and the like. For as soon as you have divided this number, you run into a number which you cannot cut. An unevenly even number is one whose parts can also be divided, but they do not reach the unit, as 24. For these divided in half make 12, and again into another half 6, then into another three; and beyond this the section receives no division, but before the unit a limit is found which you cannot cut. An unevenly odd number is one that is measured unevenly by an odd number, as 25, 49; which, though they are odd numbers, are divided also by odd parts, as seven times seven 49 and five times five 25. Of odd numbers some are simple, some composite, some middle. Simple are those which have no other part except the unit alone, as the ternary only a third, and the quinary only a fifth, and the septenary only a seventh. For these have only one part. Composite are those which are measured not only by the unit but are also produced by a foreign number, as nine, 15 and 21. For we say three threes, and seven threes, three fives, and five fives. Middle numbers are those which seem in one way simple and uncompounded, in another way also compounded; as for example nine, when compared with 25, is first and uncompounded, because it has no common number except the monad alone: but if it is compared with fifteen, it is second and compounded, since there is in it a common number besides the monad, that is, the ternary number; for it measures nine as three threes, and fifteen as three fives. Likewise of even numbers some are superabundant, some deficient, some perfect. Superabundant are those whose parts taken together exceed their fullness, for example the twelve. For it has five parts: a twelfth, which is one; a sixth, which is two; a fourth, which is three; a third, which is four; a half, which is six. For one and two and three and four and six taken together make sixteen and exceed twelve by far: so also many others like it, as eighteen, and many such. Deficient numbers are those which, reckoned by their parts, make a smaller sum, for example ten, whose parts are three: a tenth, which is one; a fifth, which is two; a half, which is five. For one and two and five taken together make eight, far less than ten. Like this is eight, and many others which, reduced to parts, stand below. A perfect number is one that is filled up by its parts, as six; for it has three parts, a sixth, a third and a half: its sixth is one, its third two, its half three. These parts brought into a sum, that is, one and two and three together, complete and perfect the same six. The perfect numbers are, within ten, 6; within a hundred, 28; within a thousand, 496.